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  • If <img alt="\Delta =\begin{vmatrix} x-2 &2x-3 &3x-4 \\ 2x-3 &3x-4 &4x-5 \\ 3x-5 &5x-8 &10x-17 \end{vmatrix}=Ax^{2}+Bx^{2}+Cx+D" src="https://entrancecorner.codecogs.com/gif.latex?%5CDelta%20%3D%5Cbegin%7Bvmatrix%7D%20x-2%2

If \Delta =\begin{vmatrix} x-2 &2x-3 &3x-4 \\ 2x-3 &3x-4 &4x-5 \\ 3x-5 &5x-8 &10x-17 \end{vmatrix}=Ax^{2}+Bx^{2}+Cx+D , then B+C is equal to:
Option: 1 -1
Option: 2 1
Option: 3 -3
Option: 4 9

Answers (1)

best_answer

\Delta =\begin{vmatrix} x-2 &2x-3 &3x-4 \\ 2x-3 &3x-4 &4x-5 \\ 3x-5 &5x-8 &10x-17 \end{vmatrix}

R_{3}\rightarrow R_{3}-R_{1}-R_{2}

=\begin{vmatrix} x-2 &2x-3 &3x-4 \\ 2x-3 &3x-4 &4x-5 \\ 0 &-1 &3x-8 \end{vmatrix}

R_{2}\rightarrow R_{2}-R_{1}

\begin{vmatrix} x-2 &2x-3 &3x-4 \\ 2x-3 &3x-4 &4x-5 \\ 0 &-1 &3x-8 \end{vmatrix}

(x-1)\begin{vmatrix} x-2 &2x-3 &3x-4 \\ 1 &1 &1 \\ 0 &-1 &3x-8 \end{vmatrix}

(x-1)\left [(x-2)-(3x-4)+(3x-8)(x-2-2x+3) \right ]

(x-1)\left [ (-2x+2)+(3x-8)(-x+1) \right ]

(x-1)\left [-3x^{2}+9x-6 \right ]

B=3+9=12

c=-6-9=-15

B+C=-3

Posted by

Suraj Bhandari

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